Systems used for image reconstruction (e.g., computed tomography (CT), phase contrast CT (or PCT), magnetic resonance imaging (MR, or MRI), etc.) can implement (potentially randomized) undersampled data acquisition in combination with compressed sensing image reconstruction to obtain viewable images from the collected scan data. This imaging can be performed for medical, preclinical, industrial, and other purposes. The collection of suitable scan data (i.e., data with a high signal to noise ratio), can expose the scan subject to large doses of radiation (i.e., for CT and PCT imaging). This exposure to radiation gives rise to concerns of increased risk of developing cancer.
Scan techniques can be implemented with lower radiation doses and/or under-sampling of data points to minimize the patient's exposure to radiation. Dedicated image reconstruction techniques are applied to this under-sampled data to generate reconstructed images of comparable image quality to images generated from non-undersampled data. Tomographic reconstruction from a limited number of scan projections can thereby be obtained. Conventional image reconstruction methods are limited to scan data without violation of the Nyquist sampling criteria and/or without the presence of substantial amounts of noise. When these conditions are not met, the accuracy of reconstructions using conventional techniques can be considerably diminished.
PCT data can be considered as four dimensional (4D), namely: phase steps, view angles, and the column/row directions of the detector. The data from the phase stepping direction is unique for PCT and requires Fourier analysis. Other approaches for processing under-sampled data can be based on interpolation of the data (typically prior to image reconstruction, i.e., as a preprocessing step) in combination with a conventional image reconstruction approach. Another approach includes compressed sensing of random under-sampling in the view-domain only for Phase Contrast CT (and not along the phase steps). Under-sampling methods can be used to speed up data acquisition and/or lower the patient x-ray dose exposure, without significant loss of image quality. For example, grating based Phase Contrast CT requires sampling in the four dimensional phase step/view angle/detector column/detector row direction.